Results for “functional regression” — Page 7

DOE OSTI2016

A novel gene expression-based prognostic scoring system to predict survival in gastric cancer

Analysis of gene expression patterns in gastric cancer (GC) can help to identify a comprehensive panel of gene biomarkers for predicting clinical outcomes and to discover potential new therapeutic targets. Here, a multi-step bioinformatics analytic approach was developed to establish a novel prognostic scoring system for GC. We first identified 276 genes that were robustly differentially expressed between normal and GC tissues, of which, 249 were found to be significantly associated with overall survival (OS) by univariate Cox regression analysis. The biological functions of 249 genes are related to cell cycle, RNA/ncRNA process, acetylation and extracellular matrix organization. A network was generated for view of the gene expression architecture of 249 genes in 265 GCs. Finally, we applied a canonical discriminant analysis approach to identify a 53-gene signature and a prognostic scoring system was established based on a canonical discriminant function of 53 genes. The prognostic scores strongly predicted patients with GC to have either a poor or good OS. Our study raises the prospect that the practicality of GC patient prognosis can be assessed by this prognostic scoring system.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Nepheline Crystallization Studies and the Structural Integrity of the Residual (SIR) - FY 2022 Study Glasses

In FY22 a set of 367 HLW glasses with compositions representative of the Waste Treatment and Immobilization Plant (WTP) processing region were aggregated and analyzed with the Structural Integrity of the Residual (SIR) model developed by the Savannah River National Laboratory (SRNL). An additional 12 glasses targeting 27 – 37 wt % alumina (in glass) and at waste loadings up to ~70 wt % were fabricated and added to the database. Collectively, this data set was analyzed with regression statistics and partitioning functions to reveal correlations between boron release and the chemical composition. FY22 results indicate that the SIR theoretical alkali-silicate precipitation term, Al 2 O 3 and B 2 O 3 concentration, and SIR computed non-bridging oxygen are significant predictors of chemical durability. A statistical model using the SIR parameters was shown to have greater overall accuracy than the nepheline discriminator model while maintaining false predictions of pour durability below 1%. In FY23, we will continue this work to focus on refining the SIR with glass compositions that challenge the SIR correlation terms, namely the theoretical crystalline precipitation and non-bridging oxygen terms.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Application and Evaluation of Surrogate Models for Radiation Source Search

Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.

Cook, Jared A.↗

NASA NTRS1977

Hot corrosion resistance of nickel-chromium-aluminum alloys

The hot corrosion resistance of nickel-chromium-aluminum alloy was examined by cyclically oxidizing sodium sulfate coated specimens in still air at 900, 1000 and 1100 C. The compositions tested were within the ternary region: Ni; Ni-50 at.% Cr; and Ni-50 at.% Al. At each temperature the corrosion data were statistically fitted to a third order regression equation as a function of chromium and aluminum contents. Corrosion isopleths were prepared from these equations. Compositional regions with the best hot corrosion resistance were identified.

Santoro, G. J.↗

NASA NTRS1977

Hot corrosion resistance of nickel-chromium-aluminum alloys

The hot corrosion resistance of nickel-chromium-aluminum alloys was examined by cyclically oxidizing sodium sulfate-coated specimens in still air at 900, 1000, and 1100 C. The compositions tested were within the ternary region: Ni, Ni-50 at.% Cr, and Ni-50 at.% Al. At each temperature the corrosion data were statistically fitted to a third order regression equation as a function of chromium and aluminum contents. From these equations corrosion isopleths were prepared. Compositional regions with the best hot corrosion resistance were identified.

Santoro, G. J.↗

NASA NTRS1980

Multispectral determination of soil moisture

The edited Guymon soil moisture data collected on August 2, 5, 14, 17, 1978 were grouped into four field cover types for statistical analysis. These are the bare, milo with rows parallel to field of view, milo with rows perpendicular to field of view and alfalfa cover groups. There are 37, 22, 24 and 14 observations respectively in each group for each sensor channel and each soil moisture layer. A subset of these data called the 'five cover set' (VEG5) limited the scatterometer data to the 15 deg look angle and was used to determine discriminant functions and combined group regressions.

Estes, J. E.↗

NASA NTRS1988

A nonparametric software reliability growth model

Miller and Sofer have presented a nonparametric method for estimating the failure rate of a software program. The method is based on the complete monotonicity property of the failure rate function, and uses a regression approach to obtain estimates of the current software failure rate. This completely monotone software model is extended. It is shown how it can also provide long-range predictions of future reliability growth. Preliminary testing indicates that the method is competitive with parametric approaches, while being more robust.

Miller, Douglas R.↗

NASA NTRS2012

Detection of Bi-Directionality in Strain-Gage Balance Calibration Data

An indicator variable was developed for both visualization and detection of bi-directionality in wind tunnel strain-gage balance calibration data. First, the calculation of the indicator variable is explained in detail. Then, a criterion is discussed that may be used to decide which gage outputs of a balance have bi- directional behavior. The result of this analysis could be used, for example, to justify the selection of certain absolute value or other even function terms in the regression model of gage outputs whenever the Iterative Method is chosen for the balance calibration data analysis. Calibration data of NASA s MK40 Task balance is analyzed to illustrate both the calculation of the indicator variable and the application of the proposed criterion. Finally, bi directionality characteristics of typical multi piece, hybrid, single piece, and semispan balances are determined and discussed.

Ulbrich, Norbert↗

NASA NTRS2018

Operator Trust Function for Predicted Drone Arrival

To realize the full benefit from autonomy, systems will have to react to unknown events and uncertain dynamic environments. The resulting number of behaviors is essentially infinite; thus, the system is effectively non-deterministic but an operator needs to understand and trust the actions of the autonomous vehicles. This research began to tackle non-deterministic systems and trust by beginning to develop a user trust function based on intent information displayed and the prescribed bounds on allowable behaviors/actions of the non-deterministic system. Linear regression shows promise on being able to predict a person’s confidence of the machine’s prediction. Linear regression techniques indicated that subject characteristics, scenario difficulty, the experience with the system, and confidence earlier in the scenario account for approximately 60% of the variation in confidence ratings. This paper details the specifics of the liner regression model – essentially a trust function – for predicting a person’s confidence.

Trujillo, Anna C.↗

NASA NTRSDate not supplied

Hybrid Model Based Approaches for Systems Health Management and Prognostics

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision making. In principle, data driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for an effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Hybrid Modeling↗

NASA NTRSDate not supplied

Systems Health Management and Prognostics Approaches for Electric Aircrafts

As more and more electric vehicles emerge in our daily operation progressively, a very critical challenge lies in the prediction of remaining driving flying time/distance for the flying vehicles. This information is important, particularly in the case of auto vehicles, because such vehicles can become self-aware, autonomously compute its own capabilities, and identify how to best plan and successfully complete vehicular missions safely. In case of electric aircrafts, computing the remaining flying time is also safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. A systematic prediction framework is implemented to identify all possible sources of uncertainty, quantify each of them individually, and mathematically estimate their combined effect on the system-level quantity of interest, in this case, the remaining flying time/distance of the unmanned aircraft. Note - This presentation contains all previously published information.

Systems Health Managent↗

NASA NTRSDate not supplied

Hybrid Approaches to Systems Health Management and Prognostics

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision making. In principle, data driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for an effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Systems Health Management↗

NASA NTRSDate not supplied

A Convolutional Neural Network for Enhancement of Multi-Scale Localization in Granular Metallic Representative Unit Cells

A convolutional neural network was used to enhance the localization of strain and stress for a generalized method of cells model of a metallic microstructure. Enhanced shear strains, measured in terms of the linear regression coefficients as a function of ground truth strains, were improved from inaccurate and uncorrelated (slope=0.003, Rsq=0.000) to accurate and well correlated (slope=0.890, Rsq=0.882) relative to ground truth (slope=1.0, Rsq=1.0). In applying the convolutional neural network, a convolutional stride of 1.0 (padding=’same’) was only modestly effective while strides of 2 or 3 were more effective yet at higher cost. Additional convolutional layers were generally more expensive than additional dense layers, often with limited benefit. The accuracy of enhanced localized shear strains and stress is expected to yield benefits for damage progression models, especially in the context of hierarchical multi-scale methods where the generalized method of cells is applied at the intermediate scale.

Machine Learning↗

NASA NTRS2022

Hybrid Model Based Approaches for Systems Health Management and Prognostics

This is a previously approved and published presentation. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Present achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. In principle, data-driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data-driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety-critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Prognostics↗

NASA NTRSDate not supplied

Health Monitoring and Prognostics for Electric Aircrafts

As more and more electric vehicles emerge in our daily operation progressively, a very critical challenge lies in the prediction of remaining driving flying time/distance for the flying vehicles. This information is important, particularly in the case of auto vehicles, because such vehicles can become self-aware, autonomously compute its own capabilities, and identify how to best plan and successfully complete vehicular missions safely. In case of electric aircrafts, computing the remaining flying time is also safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. A systematic prediction framework is implemented to identify all possible sources of uncertainty, quantify each of them individually, and mathematically estimate their combined effect on the system-level quantity of interest, in this case, the remaining flying time/distance of the unmanned aircraft. Note - This presentation contains all previously approved and published information.

Systems Health Managent↗

NASA NTRSDate not supplied

Physics Informed Neural Nets for Systems Health Management

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Development in data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. The research work presents application of physics-informed neural nets application to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived and empirical equations, integrated with connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fit driven by heuristics or empirical observations can be substituted by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This modeling strategy allows training of networks deep inside the model and unknown parameters in a single learning stage.

Physics Informed↗

DOE OSTI2021

Gaussian Kernel Methods for Seismic Fragility and Risk Assessment of Mid-Rise Buildings

Seismic fragility functions can be evaluated using the cloud analysis method with linear regression which makes three fundamental assumptions about the relation between structural response and seismic intensity: log-linear median relationship, constant standard deviation, and Gaussian distributed errors. While cloud analysis with linear regression is a popular method, the degree to which these individual and compounded assumptions affect the fragility and the risk of mid-rise buildings needs to be systematically studied. This paper conducts such a study considering three building archetypes that make up a bulk of the building stock: RC moment frame, steel moment frame, and wood shear wall. Gaussian kernel methods are employed to capture the data-driven variations in the median structural response and standard deviation and the distributions of residuals with the intensity level. With reference to the Gaussian kernels approach, it is found that while the linear regression assumptions may not affect the fragility functions of lower damage states, this conclusion does not hold for the higher damage states (such as the Complete state). In addition, the effects of linear regression assumptions on the seismic risk are evaluated. For predicting the demand hazard, it is found that the linear regression assumptions can impact the computed risk for larger structural response values. However, for predicting the loss hazard with downtime as the decision variable, linear regression can be considered adequate for all practical purposes.

58 GEOSCIENCES↗

DOE OSTI2024

Learning Functions Varying along a Central Subspace

Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of an s-Hölder function in $R^D$ which varies along a central subspace of dimension $d$ while $d \ll D$. A direct approximation of $f$ in $R^D$ with an accuracy $\varepsilon$ requires the number of samples in the order of $\varepsilon^{-(2s+D)/s}$. In this paper, we analyze the generalized contour regression (GCR) algorithm for the estimation of the central subspace and use piecewise polynomials for function approximation. GCR is among the best estimators for the central subspace, but its sample complexity is an open question. In this paper, we partially answer this questions by proving that if a variance quantity is exactly known, GCR leads to a mean squared estimation error of $O(n^{-1})$ for the central subspace. The estimation error of this variance quantity is also given in this paper. The mean squared regression error of $f$ is proved to be in the order of $(n/\log n)^{-\frac{2s}{2s+d}}$, where the exponent depends on the dimension of the central subspace instead of the ambient space . This result demonstrates that GCR is effective in learning the low-dimensional central subspace. We also propose a modified GCR with improved efficiency. Here, the convergence rate is validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗